# Exact Nondirected Angle Budgets and Thresholds

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261010-advance-20261014-r01-angle-foundations · 2026-10-10 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=0, candidate first=0. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 0)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0001/)

Angle · qf-density14-angle-split-candidate · candidate





## 2. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=45. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 45)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 45).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0002/)

Angle · qf-density14-angle-split-candidate · candidate





## 3. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=180, candidate first=30. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 150)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 150).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0003/)

Angle · qf-density14-angle-split-candidate · candidate





## 4. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=-1. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(No, 91)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (No, 91).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0004/)

Angle · qf-density14-angle-split-candidate · candidate





## 5. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=100. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(No, -10)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (No, -10).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0005/)

Angle · qf-density14-angle-split-candidate · candidate





## 6. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=84. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 6)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 6).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0006/)

Angle · qf-density14-angle-split-candidate · candidate





## 7. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=83. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 7)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 7).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0007/)

Angle · qf-density14-angle-split-candidate · candidate





## 8. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=82. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 8)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 8).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0008/)

Angle · qf-density14-angle-split-candidate · candidate





## 9. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=81. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 9)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 9).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0009/)

Angle · qf-density14-angle-split-candidate · candidate





## 10. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=80. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 10)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 10).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0010/)

Angle · qf-density14-angle-split-candidate · candidate





## 11. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=79. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 11)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 11).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0011/)

Angle · qf-density14-angle-split-candidate · candidate





## 12. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=78. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 12)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 12).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0012/)

Angle · qf-density14-angle-split-candidate · candidate





## 13. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=77. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 13)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 13).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0013/)

Angle · qf-density14-angle-split-candidate · candidate





## 14. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=76. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 14)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 14).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0014/)

Angle · qf-density14-angle-split-candidate · candidate





## 15. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=75. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 15)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 15).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0015/)

Angle · qf-density14-angle-split-candidate · candidate





## 16. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=74. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 16)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 16).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0016/)

Angle · qf-density14-angle-split-candidate · candidate





## 17. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=73. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 17)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 17).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0017/)

Angle · qf-density14-angle-split-candidate · candidate





## 18. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=72. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 18)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 18).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0018/)

Angle · qf-density14-angle-split-candidate · candidate





## 19. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=71. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 19)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 19).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0019/)

Angle · qf-density14-angle-split-candidate · candidate





## 20. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=70. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 20)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 20).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0020/)

Angle · qf-density14-angle-split-candidate · candidate





## 21. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=69. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 21)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 21).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0021/)

Angle · qf-density14-angle-split-candidate · candidate





## 22. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=68. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 22)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 22).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0022/)

Angle · qf-density14-angle-split-candidate · candidate





## 23. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=67. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 23)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 23).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0023/)

Angle · qf-density14-angle-split-candidate · candidate





## 24. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=66. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 24)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 24).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0024/)

Angle · qf-density14-angle-split-candidate · candidate





## 25. Angle-Split Eligibility and Signed Remainder

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=65. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.

View answer and explanation(Yes, 25)

Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 25).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0025/)

Angle · qf-density14-angle-split-candidate · candidate





## 26. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=0. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 90, 180)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 90, 180).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0026/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 27. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=90. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 0, 90)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 0, 90).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0027/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 28. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=180. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(No, none, 0)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (No, none, 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0028/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 29. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=4. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 86, 176)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 86, 176).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0029/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 30. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=5. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 85, 175)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 85, 175).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0030/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 31. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=6. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 84, 174)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 84, 174).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0031/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 32. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=7. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 83, 173)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 83, 173).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0032/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 33. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=8. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 82, 172)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 82, 172).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0033/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 34. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=9. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 81, 171)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 81, 171).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0034/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 35. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=10. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 80, 170)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 80, 170).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0035/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 36. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=11. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 79, 169)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 79, 169).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0036/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 37. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=12. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 78, 168)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 78, 168).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0037/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 38. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=13. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 77, 167)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 77, 167).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0038/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 39. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=14. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 76, 166)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 76, 166).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0039/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 40. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=15. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 75, 165)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 75, 165).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0040/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 41. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=16. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 74, 164)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 74, 164).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0041/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 42. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=17. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 73, 163)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 73, 163).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0042/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 43. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=18. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 72, 162)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 72, 162).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0043/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 44. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=19. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 71, 161)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 71, 161).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0044/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 45. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=20. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 70, 160)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 70, 160).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0045/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 46. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=21. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 69, 159)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 69, 159).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0046/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 47. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=22. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 68, 158)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 68, 158).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0047/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 48. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=23. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 67, 157)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 67, 157).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0048/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 49. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=24. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 66, 156)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 66, 156).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0049/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 50. Complement Eligibility and Supplement

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=25. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).

View answer and explanation(Yes, 65, 155)

Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 65, 155).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0050/)

Angle · qf-density14-angle-complement-supplement-pair · candidate





## 51. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=0, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-90, -180, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-90, -180, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0051/)

Angle · qf-density14-angle-pair-defects · candidate





## 52. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=45, b=45. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(0, -90, Yes, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (0, -90, Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0052/)

Angle · qf-density14-angle-pair-defects · candidate





## 53. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=90, b=90. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(90, 0, No, Yes)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (90, 0, No, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0053/)

Angle · qf-density14-angle-pair-defects · candidate





## 54. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=180, b=180. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(270, 180, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (270, 180, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0054/)

Angle · qf-density14-angle-pair-defects · candidate





## 55. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=4, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-86, -176, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-86, -176, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0055/)

Angle · qf-density14-angle-pair-defects · candidate





## 56. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=5, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-85, -175, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-85, -175, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0056/)

Angle · qf-density14-angle-pair-defects · candidate





## 57. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=6, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-84, -174, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-84, -174, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0057/)

Angle · qf-density14-angle-pair-defects · candidate





## 58. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=7, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-83, -173, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-83, -173, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0058/)

Angle · qf-density14-angle-pair-defects · candidate





## 59. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=8, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-82, -172, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-82, -172, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0059/)

Angle · qf-density14-angle-pair-defects · candidate





## 60. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=9, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-81, -171, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-81, -171, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0060/)

Angle · qf-density14-angle-pair-defects · candidate





## 61. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=10, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-80, -170, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-80, -170, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0061/)

Angle · qf-density14-angle-pair-defects · candidate





## 62. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=11, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-79, -169, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-79, -169, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0062/)

Angle · qf-density14-angle-pair-defects · candidate





## 63. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=12, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-78, -168, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-78, -168, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0063/)

Angle · qf-density14-angle-pair-defects · candidate





## 64. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=13, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-77, -167, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-77, -167, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0064/)

Angle · qf-density14-angle-pair-defects · candidate





## 65. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=14, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-76, -166, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-76, -166, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0065/)

Angle · qf-density14-angle-pair-defects · candidate





## 66. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=15, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-75, -165, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-75, -165, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0066/)

Angle · qf-density14-angle-pair-defects · candidate





## 67. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=16, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-74, -164, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-74, -164, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0067/)

Angle · qf-density14-angle-pair-defects · candidate





## 68. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=17, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-73, -163, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-73, -163, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0068/)

Angle · qf-density14-angle-pair-defects · candidate





## 69. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=18, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-72, -162, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-72, -162, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0069/)

Angle · qf-density14-angle-pair-defects · candidate





## 70. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=19, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-71, -161, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-71, -161, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0070/)

Angle · qf-density14-angle-pair-defects · candidate





## 71. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=20, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-70, -160, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-70, -160, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0071/)

Angle · qf-density14-angle-pair-defects · candidate





## 72. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=21, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-69, -159, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-69, -159, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0072/)

Angle · qf-density14-angle-pair-defects · candidate





## 73. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=22, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-68, -158, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-68, -158, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0073/)

Angle · qf-density14-angle-pair-defects · candidate





## 74. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=23, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-67, -157, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-67, -157, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0074/)

Angle · qf-density14-angle-pair-defects · candidate





## 75. Two Angle-Sum Threshold Defects

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=24, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).

View answer and explanation(-66, -156, No, No)

Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-66, -156, No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0075/)

Angle · qf-density14-angle-pair-defects · candidate





## 76. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[0, 0, 0], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([0, 0, 0], Yes, 180)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([0, 0, 0], Yes, 180).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0076/)

Angle · qf-density14-angle-three-part-budget · candidate





## 77. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[90, 90, 0], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([90, 180, 180], Yes, -90)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([90, 180, 180], Yes, -90).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0077/)

Angle · qf-density14-angle-three-part-budget · candidate





## 78. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[90, 90, 90], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([90, 180, 270], No, -90)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([90, 180, 270], No, -90).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0078/)

Angle · qf-density14-angle-three-part-budget · candidate





## 79. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[180, 1, 0], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([180, 181, 181], No, -91)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([180, 181, 181], No, -91).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0079/)

Angle · qf-density14-angle-three-part-budget · candidate





## 80. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[4, 90, 5], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([4, 94, 99], Yes, 81)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([4, 94, 99], Yes, 81).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0080/)

Angle · qf-density14-angle-three-part-budget · candidate





## 81. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[5, 90, 6], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([5, 95, 101], Yes, -11)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([5, 95, 101], Yes, -11).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0081/)

Angle · qf-density14-angle-three-part-budget · candidate





## 82. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[6, 90, 7], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([6, 96, 103], Yes, 77)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([6, 96, 103], Yes, 77).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0082/)

Angle · qf-density14-angle-three-part-budget · candidate





## 83. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[7, 90, 8], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([7, 97, 105], Yes, -15)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([7, 97, 105], Yes, -15).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0083/)

Angle · qf-density14-angle-three-part-budget · candidate





## 84. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[8, 90, 9], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([8, 98, 107], Yes, 73)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([8, 98, 107], Yes, 73).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0084/)

Angle · qf-density14-angle-three-part-budget · candidate





## 85. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[9, 90, 10], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([9, 99, 109], Yes, -19)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([9, 99, 109], Yes, -19).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0085/)

Angle · qf-density14-angle-three-part-budget · candidate





## 86. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[10, 90, 11], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([10, 100, 111], Yes, 69)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([10, 100, 111], Yes, 69).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0086/)

Angle · qf-density14-angle-three-part-budget · candidate





## 87. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[11, 90, 12], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([11, 101, 113], Yes, -23)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([11, 101, 113], Yes, -23).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0087/)

Angle · qf-density14-angle-three-part-budget · candidate





## 88. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[12, 90, 13], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([12, 102, 115], Yes, 65)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([12, 102, 115], Yes, 65).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0088/)

Angle · qf-density14-angle-three-part-budget · candidate





## 89. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[13, 90, 14], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([13, 103, 117], Yes, -27)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([13, 103, 117], Yes, -27).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0089/)

Angle · qf-density14-angle-three-part-budget · candidate





## 90. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[14, 90, 15], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([14, 104, 119], Yes, 61)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([14, 104, 119], Yes, 61).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0090/)

Angle · qf-density14-angle-three-part-budget · candidate





## 91. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[15, 90, 16], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([15, 105, 121], Yes, -31)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([15, 105, 121], Yes, -31).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0091/)

Angle · qf-density14-angle-three-part-budget · candidate





## 92. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[16, 90, 17], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([16, 106, 123], Yes, 57)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([16, 106, 123], Yes, 57).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0092/)

Angle · qf-density14-angle-three-part-budget · candidate





## 93. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[17, 90, 18], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([17, 107, 125], Yes, -35)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([17, 107, 125], Yes, -35).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0093/)

Angle · qf-density14-angle-three-part-budget · candidate





## 94. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[18, 90, 19], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([18, 108, 127], Yes, 53)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([18, 108, 127], Yes, 53).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0094/)

Angle · qf-density14-angle-three-part-budget · candidate





## 95. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[19, 90, 20], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([19, 109, 129], Yes, -39)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([19, 109, 129], Yes, -39).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0095/)

Angle · qf-density14-angle-three-part-budget · candidate





## 96. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[20, 90, 21], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([20, 110, 131], Yes, 49)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([20, 110, 131], Yes, 49).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0096/)

Angle · qf-density14-angle-three-part-budget · candidate





## 97. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[21, 90, 22], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([21, 111, 133], Yes, -43)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([21, 111, 133], Yes, -43).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0097/)

Angle · qf-density14-angle-three-part-budget · candidate





## 98. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[22, 90, 23], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([22, 112, 135], Yes, 45)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([22, 112, 135], Yes, 45).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0098/)

Angle · qf-density14-angle-three-part-budget · candidate





## 99. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[23, 90, 24], target=90. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([23, 113, 137], Yes, -47)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([23, 113, 137], Yes, -47).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0099/)

Angle · qf-density14-angle-three-part-budget · candidate





## 100. Three-Part Prefix Budget and Eligibility

Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[24, 90, 25], target=180. Give (three prefix sums, is the total≤180?, target−total).

View answer and explanation([24, 114, 139], Yes, 41)

Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([24, 114, 139], Yes, 41).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261010-advance-20261014-r01-angle-0100/)

Angle · qf-density14-angle-three-part-budget · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261010-advance-20261014-r01-angle-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261010-advance-20261014-r01-angle-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261010-advance-20261014-r01-angle-foundations/validation-report.json)